1. Field of the Invention
The present invention relates to a measurement apparatus which measures the position of a measurement target object.
2. Description of the Related Art
In precision machining and an inspection process, the position or displacement of a measurement target object needs to be measured at nm to μm-order accuracy, and a measurement apparatus using the principle of an interferometer is often used. Of such measurement apparatuses, a heterodyne interferometer is used for high-accuracy length measurement. The heterodyne interferometer detects a reference signal modulated at a frequency fr and a measurement signal which is modulated at the frequency fr and contains position information of a measurement target object. The measurement signal contains a frequency shift fd caused by a Doppler shift corresponding to the moving speed of a measurement target object in addition to a shift of the frequency fr caused by modulation. Thus, the frequencies of the measurement signals are (fr±fd). Frequencies±fd are detected by calculating the differences between the frequencies of the reference signal and measurement signals. The frequency difference of ±fd is time-integrated to calculate the phase difference, and the position or displacement of the measurement target object is calculated from the calculated phase difference.
Japanese Patent Laid-Open No. 5-346305 discloses a conventional heterodyne interferometer. The heterodyne interferometer generates the beat frequency between a reference signal and a measurement signal using a mixer, temporally measures its phase change, and calculates a position or displacement. In this case, ps-order time measurement is required to obtain nm-order measurement accuracy. However, it is difficult to improve the time resolution and maintain stability, and an increase in measurement accuracy is limited. Japanese Patent Laid-Open No. 2008-510170 discloses a heterodyne interferometer which detects an interference signal using an A/D converter instead of time measurement. The heterodyne interferometer disclosed in Japanese Patent Laid-Open No. 2008-510170 detects a reference signal and measurement signal using, for example, an 120-MHz A/D converter, and performs DFT (Discrete Fourier Transform) calculation in every 10 MHz. The heterodyne interferometer disclosed in Japanese Patent Laid-Open No. 2008-510170 further performs CORDIC (Coordinate Rotation Digital Computer) calculation to calculate a phase and measure a position or displacement.
In phase detection using a heterodyne interferometer, a method of calculating the position or displacement of a measurement target object by high-speed A/D conversion and digital signal processing for a reference signal and measurement signal is superior for higher accuracy to the ps-order time measurement method. However, the heterodyne interferometer disclosed in Japanese Patent Laid-Open No. 2008-510170 requires ultra-high-speed, large-scale digital signal processing in real time in addition to high-speed A/D conversion because of the following reason. In general, DFT is known to require an enormous amount of calculation. DFT for N data requires N2 complex multiplications and N×(N−1) complex additions. For example, DFT for N=72 data requires 5,184 complex multiplications and 5,112 complex additions. To execute this calculation in every 10 MHz, an ultra-high-speed DSP (Digital Signal Processor) or FPGA (Field Programmable Gate Array) is used, and large-scale parallel calculation of ultra-high-speed multiplication and addition is necessary. For this reason, the cost, heat generation amount, and operation load increase in the digital signal processing unit of the heterodyne interferometer disclosed in Japanese Patent Laid-Open No. 2008-510170.